Time: 20 minutes. This quiz is open book, open notes.
1. A batch A has the summary statistics listed below. The values in batch B are obtained by dividing each value in A by 2 and then adding 10. Compute the corresponding summary statistics for B. In cases where it is not possible to deduce the value, or if the value is not defined, then please so indicate.
| Statistic | A | B |
| Count | 143 | |
| Median | 16.0 | |
| H-spread | 24.2 | |
| 90th percentile | 97.6 | |
| Variance | 1,032 | |
| Third order statistic (X[3]) | 0.8 | |
| Geometric mean | 11.2 | |
| 10% Trimmed mean | 18.4 |
Would you expect A to be positively skewed, negatively skewed, or have approximately zero skewness? What about B?
2. Draw a histogram of the following batch of arsenic measurements in soil (mg/Kg dry weight). Use whole powers of two for the cutpoints: that is, put the bin endpoints at 1, 2, 4, 8, 16, and 32 mg/Kg. The values have been sorted for you and grouped into sets of five for more reliable reading.
(1.5, 2.1, 2.5, 2.7, 2.8,
3.6, 4.6, 4.6, 4.9, 5.0,
5.2, 5.4, 5.5, 5.5, 5.6,
5.8, 5.8, 6.4, 6.7, 6.7,
6.8, 7.1, 7.3, 7.3, 7.8,
8.1, 9.1, 9.2, 9.3, 10.2,
11.0, 11.6, 12.1, 12.4, 13.9,
15.3, 16.0, 17.0, 24.7, 27.2)
Label the histogram appropriately so that it can be read on its own. Use relative frequency on the y-axis.
3. A batch has 24 values. The five largest values are 33.0, 24.6, 17.0, 16.0, and 15.3 Compute the 90th percentile of this batch. Use Weibull plotting positions (text, page 96). Round the answer to one decimal place precision (the same as the data).
Scoring: The passing score is 96.
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